Permanent magnet arrangement for generating a homogeneous field (&#34;3d halbach&#34;)

ABSTRACT

A magnet arrangement (1) in a magnetic resonance apparatus having a permanent magnet system for generating a homogeneous magnetic field in a direction perpendicular to a z-axis in a measurement volume. The magnet system has at least two ring-shaped magnet elements (2) in a ring plane, which are arranged coaxially around the z-axis and are constructed from individual magnet segments (3) arranged next to one another in a Halbach configuration. The magnetization direction of at least two ring-shaped magnet elements deviates from the ring plane such that the component perpendicular to the ring plane varies cosinusoidally with the azimuthal angle of the respective ring-shaped magnet element. The magnetization of in each case two ring-shaped magnet elements is mirror-symmetrical with respect to one another, wherein the mirror plane is the central x-y-plane perpendicular to the z-axis. The disclosed arrangement provides a compact and lightweight permanent magnet arrangement for an MR apparatus.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims foreign priority under 35 U.S.C. § 119(a)-(d) toGerman Application No. 10 2018 214 213.0 filed on Aug. 22, 2018, theentire contents of which are hereby incorporated into the presentapplication by reference.

FIELD OF THE INVENTION

The invention relates to a magnet arrangement in a magnetic resonanceapparatus having a permanent magnet system for generating a homogeneousmagnetic field in a direction perpendicular to a z-axis in a measurementvolume, wherein the permanent magnet system comprises at least tworing-shaped magnet elements containing magnetic material in a ringplane, which are arranged coaxially around the z-axis and areconstructed from individual magnet segments arranged in a Halbachconfiguration, wherein the magnetization direction of at least tworing-shaped magnet elements deviates from the ring plane in such a waythat the component perpendicular to the ring plane varies with theazimuthal angle of the ring, and a 3D angle α determines the deviationof the magnetization directions from those of a planar Halbach ring, andwherein the magnetization of in each case two ring-shaped magnetelements is mirror-symmetrical with respect to one another, and themirror plane is the central x-y-plane perpendicular to the z-axis.

BACKGROUND

Such a magnet arrangement is known from U.S. Pat. No. 10,018,694 B2(=reference [1]).

The present invention relates generally to the field of magnetconstruction, in particular the production and operation of magnetarrangements. The invention, however, also relates to the field ofmagnetic resonance (MR), in particular to providing permanent magnetsystems which are suitable therefor and which are intended forgenerating homogeneous magnetic fields for NMR measurements. However,the applicability of the invention is not restricted to these fields.

Both in the field of nuclear magnetic resonance (NMR) spectroscopy andin the imaging application (MRI), a very homogeneous magnetic field thatis constant over time is required in a sample volume to be defined,which magnetic field can be generated by resistive or superconductingcoils or a suitable permanent magnet arrangement. The use of permanentmagnets is preferred if flux densities of less than 2 T are sufficientand a comparatively compact construction is desired.

Benchtop NMR apparatuses require an extremely homogeneous magneticfield, which can be generated for instance by a superconducting magnetcoil arrangement, but also by a permanent magnet arrangement.

The Halbach design is a known arrangement that can be used for thispurpose. The use of ring-shaped permanent magnets having a magnetizationas a Halbach dipole is described in the prior art (see, for instance,reference [2]).

In theory, the high field homogeneity required for NMR measurements canalso be achieved using these magnet arrangements, but, precisely in thecase of magnet rings in a Halbach configuration, it is very difficult togenerate such a homogeneous B0 field. Ring-shaped Halbach dipoles aretypically constructed in such a way that individual magnet segmentshaving varying magnetization directions are joined together, themagnetization direction varying in azimuthal angle.

In order to achieve the field homogeneity demanded for NMR measurementsin the sample volume, in the case of the yoke-free Halbach magnets,correction mechanisms must be provided in order to be able to compensatefor tolerances of the magnet material or of the position of theindividual magnet blocks, which complicates the mechanical construction.Yoke-based magnets generally have a parallel pole shoe pair composed ofa soft-magnetic material having a correspondingly high saturation fluxdensity. Through a suitable choice of the pole shoe geometry andspecific surface processing, the field profile can be optimized in acomparatively simple and efficient manner.

The main causes which obstruct field homogeneity can be summarized asfollows:

1. Finiteness of the arrangement in an axial direction, that is to sayfundamental deviation from a cylinder extended infinitely in an axialdirection.2. Discretization of the magnetization direction along the cylindercircumference, that is to say fundamental deviation from themagnetization direction varying continuously with the azimuthal angle.3. Additional disturbances resulting from mechanical tolerances forsize, positioning and magnetic moment of the magnet segments.

Specific Prior Art

U.S. Pat. No. 4,837,542 A (=reference [3]) discloses a sphericalpermanent magnet constructed from individual segments, wherein thesegments are tapered in a wedge-shaped fashion towards the midpoint andbecome smaller towards the pole regions (sphere segments). Theconstruction of such a Halbach sphere is very complex; a constructioncomposed of planar rings having geometrically identical segments is notdisclosed. The magnetization direction of the individual segments in arevolution around the sphere is in a traditional Halbach configuration(α=2θ). The central hole of the magnet extends longitudinally along thepolar axis in the direction of the B0 field. In the case of planarHalbach magnets constructed from segmented rings, the hole extendstransversely, that is to say perpendicularly to the direction of thecentral field. In the case of a longitudinal hole, the B0 field is lowerand thus less effective. Moreover, the basic magnet according toreference [3] generally generates an inhomogeneous magnetic field.

US 2015/0061680 A1 (=reference [4]) describes magnet arrangements andmethods for generating magnetic fields. It encompasses magnetarrangements having a plurality of polyhedral magnets which are arrangedin a lattice configuration and at least partly enclose a testing volume,wherein the magnet arrangement has an associated magnetic field with adesignated field direction. The magnetization direction of theindividual polyhedral magnets and the arrangement thereof are such thatthe resulting magnetic field approximates a Halbach sphere. In otherwords, arrangements are described in which the magnetization directionscorrespond to those of the three-dimensional Halbach design. Cylindricalrings are not mentioned, however; only the polyhedral magnet segmentsare joined together. Moreover, the field of the basic magnet accordingto the method described here is generally not homogeneous and is thusunsuitable for MR applications.

The simple Halbach design requires a large axial length and thus a largeamount of magnet material in order to generate a field with sufficienthomogeneity. Even a planar Halbach design having notches still requiresan unnecessarily large amount of magnet material since the parts of themagnet that are axially far away have an unfavourable magnetizationdirection with regard to the field contribution thereof at the samplelocation.

US 2010/013473 A1 (=reference [2]) proposes an NMR permanent magnethaving a Halbach architecture composed of three rings, with a centralmagnet ring being flanked by two head rings. The rings are mutuallydisplaceable in a longitudinal direction with screws or threaded nutsfor the purpose of field homogenization. US 2010/013473 A1 furthermorediscloses the fact that the rings consist of individual segments thatare alternately trapezoidal and rectangular, wherein the individualsegments are displaceable in a radial direction for the purpose of fieldhomogenization. This magnet has 64 mechanical degrees of freedom.Setting them is in any case rather complex. The magnetization of theindividual segments only ever varies in the azimuthal direction and hasno angle component pointing out of the plane of the respective magnetrings.

U.S. Pat. No. 10,018,694 B2 (=reference [1]), cited in the introduction,proposes a magnetic resonance apparatus with a permanent magnet system.Cuboidal magnets are arranged annular on the housing of the magneticresonance apparatus to generate a homogeneous magnetic field in ameasuring volume. The Halbach-like orientation of the magnetizationswith respect to the measuring volume is achieved by an alternatingorientation of the respective magnets in the housing. The cuboid magnetsare uniformly magnetized with respect to their surfaces. This magneticresonance apparatus has the disadvantage that it is expensive to create,since the expression of the holding receptacles in the housing for theindividual magnets must be very precise for orientation according to theHalbach-condition. In addition, a low efficiency is achieved withrespect to the achievable magnetic field strength by the spatialdistance of the magnets to the measuring volume. Due to the cuboid shapeof the individual magnets, a compact design is also not possible.

SUMMARY

Against that background, it is an object of the present invention toprovide, using simple technical measures and with no increase in volume,a maximally compact and lightweight permanent magnet arrangement of thetype defined in the introduction for an MR apparatus which—for apredefined field strength—has, at least in most regions of the magnet, amagnetization direction that is advantageous with regard to its fieldcontribution at the sample location, and which simultaneously producesthere a region having a particularly homogeneous field distributionand—particularly for high field strengths—a lowest possible leakagefield.

This object is achieved by the present invention, in a manner that isjust as surprisingly simple as it is effective, by virtue of (i) thering-shaped magnet elements being constructed from magnet segmentsarranged next to one another and being composed of magnetic material,and (ii) the magnetization direction of the magnet segments with respectto their outer surfaces parallel to the respective ring plane beingdifferent in each case from that of the two magnet segments adjacent inthe ring-shaped magnet element.

The invention includes arrangements of three-dimensional Halbach ringswith the aim of generating a magnetic field that is homogeneous to thegreatest possible extent in a predefined sample volume with as littlematerial as possible being used. A three-dimensional (3D) Halbach ringarises from a traditional planar Halbach ring by rotating themagnetization vectors about the direction of the azimuthal vector by a3D angle α, a parameter fixed for the entire magnet ring. These ringsare arranged such that the magnetization directions are orientedadvantageously for amplifying the main field almost in the entire magnetsystem. Only in small regions near the sample are larger deviations fromthis advantageous orientation of the magnetization permitted, in orderto improve the homogeneity of the field in the sample volume.

A central advantage of the arrangements of three-dimensional Halbachrings according to the invention is that the magnetic field strength ishigher in comparison with planar Halbach rings, with the same amount ofmaterial being used. If consideration is given to a planar Halbachmagnet extended infinitely in an axial direction, for example, then amagnetic field B0 of Br*log(r_(a)/r_(i)) results, wherein Br is theremanence of the magnet material, r_(a) is the external radius and r_(i)is the internal radius of the magnet ring, and a B0 of4/3*Br*log(r_(a)/r_(i)) results for the optimized 3D Halbach (α=2*polarangle−π), wherein the polar angle is the angle between the spatialvector of the magnet element respectively considered and the hole axis.The 3D Halbach is thus stronger than the planar Halbach potentially by afactor of 4/3, with the same amount of material being used.

A permanent magnet system according to the present invention comprisestwo or more three-dimensional Halbach rings having a common axis. Inthis case, a three-dimensional Halbach ring is a ring composed ofhard-magnetic material having a rectangular cross section.

The dimensions of the rings, their relative positions with respect toone another and their 3D angles are chosen such that the on-axis (zonal)field orders vanish up to a predefined order, the “design order”, and atthe same time the value of the central field is maximized. The off-axis(tesseral) field orders then likewise vanish up to the predefined order.

In the case of Halbach rings (irrespective of whether planar or 3DHalbach), only zonal and doubly periodic (tesseral) field orders occur,in principle. Furthermore, there is a proportional relationship betweenthe zonal (=on-axis) and doubly periodic, i.e. tesseral (=off-axis),terms of identical order n, wherein the proportionality factor isdependent on n. An arrangement of Halbach rings configured such that aspecific zonal term vanishes thus also has no tesseral terms of thisorder. Both properties (in principle only doubly periodic terms andproportional relationship between zonal and doubly periodic terms) werederived from Maxwell's equations for planar Halbach rings and werechecked for 3D Halbach rings, which was not generally known previously.

The remaining inhomogeneities having orders less than or equal to thedesign order are then attributable to mechanical tolerances and materialinhomogeneities and can be corrected using known shim technologies.

Each three-dimensional Halbach ring consists of uniform permanent magnetmaterial. The material of different rings can be different here.

Preferred Embodiments and Developments of the Invention

Particular preference is given to a class of embodiments of the magnetarrangement according to the invention in which the magnet segments areconstructed such that the magnetization direction of the individualmagnet segments follows the formula

Mr=M Cos[α]Cos[ϕ0], Mϕ=M Sin[ϕ0], Mz=M Cos[ϕ0] Sin[α],

wherein the components of the magnetization vector in cylindricalcoordinates denote:M the remanence of the magnet material used in the respective magnetring,ϕ0 the azimuthal angle of the segment midpoint, andα a parameter fixed for the entire magnet ring, namely the 3D angle thatdetermines the deviation of the magnetization directions from those of aplanar Halbach ring.

Given a suitable choice of the ring dimensions, the ring positions andthe 3D angles, an approximation to a 3D Halbach arrangement as inreference [3] results, but with a transverse hole, that is to say a holeperpendicular to the field direction. This arrangement is more effectivethan a longitudinally drilled 3D Halbach having a hole in the fielddirection, that is to say generates more field with the same amount ofmagnet material being used.

Further advantageous embodiments are characterized in that the magnetsegments are produced from a hard-magnetic material having a highremanence M, wherein 1.5 T>M>0.7 T, and having a low permeability μ inthe range of 1.0<μ<1.5, in particular from NdFeB. Thus, it is possibleto achieve high field strengths in conjunction with low weight andreciprocal influencing of the magnet parts remains low.

A further advantageous embodiment provides for the magnet segmentsarranged in a region of high field strengths to be produced from ahigh-coercivity material having a coercivity HcJ in the range of 2800kA/m>HcJ>1500 kA/m. The risk of partial demagnetization is significantlyreduced as a result.

One preferred embodiment of the invention is characterized in that themagnet segments are produced from a temperature-compensated permanentmagnet material having a temperature coefficient Tk in the range of0%/K>Tk>−0.05%/K, in particular from SmCo. In this way, the magnetbecomes more thermostable and the effort required for temperatureregulation decreases.

A class of particularly preferred embodiments of the magnet arrangementaccording to the invention is distinguished by the fact that besides themirror-symmetrical 3D Halbach rings, one or more of the ring-shapedmagnet elements is/are constructed as a planar Halbach ring where α=0.The additional planar Halbach rings serve principally to amplify the B0field further. Preferably, this is a central ring surrounded by twomirror-symmetrical 3D Halbach rings. What is primarily advantageous isthat no interfaces occur in the central region near the sample, saidinterfaces always being associated with inaccuracies and thus withdisturbances of the homogeneity. However, it is also conceivable for the3D Halbach rings to be flanked by planar Halbach rings where α=0.

In a class of supplementary or alternative embodiments, besides themirror-symmetrical 3D Halbach rings, one or more of the ring-shapedmagnet elements is/are constructed as a laterally homogeneouslymagnetized ring where α=π. A laterally homogeneously magnetized ring canbe constructed from segments like an arbitrary three-dimensional Halbachring. Owing to the uniform magnetization direction, however, there isalso the possibility of manufacturing said ring from a continuous tubethat is subsequently magnetized in one piece. These laterallyhomogeneously magnetized rings where α=π are preferably arranged inregions near the hole, that is to say in inner areas concentrically.

In both classes of embodiments, the arrangement can be producedparticularly simply, fewer mutually different types of segments existand a higher symmetry thus also results.

Also particularly advantageous are embodiments of the invention whichare distinguished by the fact that the ring-shaped magnet elements areconstructed such that far field coefficients of low order n≤6, inparticular the dipole moment, vanish. The leakage field of the magnetarrangement can thus be considerably reduced during operation.

Also well proven in practice are embodiments which are characterized inthat the ring-shaped magnet elements are arranged concentrically aroundthe z-axis, and in that the radially inner ring-shaped magnet elementhas a higher coercive field strength than the radially outer ring-shapedmagnet elements. This is expedient particularly if there are more thantwo rings present which are constructed concentrically in pairs and themagnet pair rings are arranged coaxially with respect to one another.The risk of partial demagnetization is reduced as a result.

In embodiments which are particularly simple and inexpensive to produce,the magnet segments of each annular magnet element have the same outershape.

For geometrical reasons, embodiments of the invention are advantageousin which magnet segments of each ring-shaped magnet element have theshape of a trapezoidal prism. Such trapezoidal prisms are particularlyeasy to assemble into a roughly hollow cylindrical annulus.

Particularly high magnetic field strengths or a particular compactnessof the arrangement can be achieved with embodiments in which the magnetsegments of each ring-shaped magnet element are arranged directlyadjacent to each other in the assembled state.

Within each ring-shaped magnet element, the magnet segments consist ofuniform permanent magnet material. The magnet segments are preferablydirectly adjacent within the ring-shaped magnet elements, in particular,the gaps between the magnet segments are substantially smaller than theouter dimensions of the magnet segments. To stabilize the ring-shapedmagnet elements, the gaps are advantageously filled with an adhesive.

In addition, the magnet segments are advantageously disposed within themagnetic elements symmetrically with respect to the z-axis, i.e. arotation of the ring-shaped magnet element by the angular range of amagnet segment with respect to the z-axis converts the structure but notnecessarily the magnetization direction of the ring-shaped magnetelement itself. Furthermore, the direction of magnetization of adjacentmagnet segments in the ring-shaped magnet elements also varies withrespect to the outer shape of the magnet segments. Prior to assemblingof the magnet segments into ring-shaped magnet elements, adjacent magnetsegments must be individually magnetized in a different direction withrespect to their outer shape, wherein the direction being chosen is incompliance with the 3D angle α and the Halbach-angle.

Magnetic materials often have a preferred axis along which amagnetization can be particularly effective. Therefore, it isadvantageous if the individual magnet segments are individually formedfrom the magnetic material such that this preferred axis extends in thedirection of the magnetization direction to be taken for the arrangementin the ring-shaped magnet element.

In general, the ring-shaped magnet elements will be arranged in a mannerstacked one above another in the z-direction, wherein the permanentmagnet system has at least two ring-shaped magnet elements and thering-shaped magnet elements are fixedly adhesively bonded as a whole andare displaceable laterally relative to one another as a whole. Thisarrangement enables the individual ring assemblies (optionally composedof different materials) to be mounted as self-contained assemblies incontrast to the Halbach sphere in accordance with reference [3].

Particular preference is given to an embodiment of the magnetarrangement according to the invention in which the ring-shaped magnetelements are mounted rotatably about the z-axis. Production-dictatedfluctuations of the segments combined in a ring-shaped fashion may bringabout an angular deviation of the magnetic axis of an entire ring. Theembodiment described makes it possible to correct this angular deviationby setting a corresponding angle in the opposite sense.

Particular preference is given to embodiments of the invention whichcomprise a device for homogenizing the magnetic field, preferably a shimtube, for shimming the higher field orders. In this way, the mechanismsdescribed beforehand are supplemented by a further, even more preciseinstrument for homogenization. Corrections with even finer resolutionare thus possible.

Using passive shim elements, the homogeneity in the interior of themagnet hole, in particular in a shim tube, can be significantlyimproved. Moreover, an improvement in the homogeneity can also beachieved with electrical shim coils in the interior of the hole.

The scope of the present invention also encompasses a method forproducing a magnet arrangement in accordance with the above-describedembodiments or the developments thereof, comprising:

a) predefining a target magnetic field B0 and the required number ofmagnet rings composed of known magnet material and a desired internaldiameter of the central hole;b) determining the desired homogeneity and leakage field properties byequating to zero at least one field order of the central or far fieldexpansion;c) determining the free design parameters, namely geometry parameters ofthe rings and 3D angles α of the rings, by optimizing the magnet volumeunder the constraints from steps a) and b);d) determining the desired weight as a function of the design parametersdetermined under step c).

In one advantageous variant of the method according to the invention, instep c) the field orders and the magnet volume are calculated directlyfrom the design parameters by way of analytical formulae. In this way,the optimization calculation proceeds particularly rapidly and extensiveparameter studies are made possible.

In a further preferred method variant, the individual magnet segmentsare produced in the defined magnetization direction in a mannercomplying with the 3D angle α and the Halbach angle before they areassembled to form magnet rings. The segments have the predefineddimensions such as are predefined in step a) and were determined insteps c) and d). The number of segments per ring is preferably between 8and 32, particularly preferably from 16 to 24. The number of segmentsper ring is crucial for the off-axis homogeneity. Moreover, a highernumber of segments brings about a greater approximation to the designfield strength.

Further advantages of the invention are evident from the description andthe drawing. Likewise, the features mentioned above and those that willbe explained further can be used according to the invention in each caseindividually by themselves or as a plurality in arbitrary combinations.The embodiments shown and described should not be understood as anexhaustive enumeration, but rather are of exemplary character foroutlining the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is illustrated in the figures and diagrams of the drawingssection and is explained in greater detail on the basis of exemplaryembodiments.

In the figures:

FIG. 1A shows a schematic spatial vertical sectional half-illustrationof a simple embodiment of the magnet arrangement according to theinvention having two ring-shaped magnet elements arrangedmirror-symmetrically with respect to the xy-plane, and having 3D Halbachmagnetization of the individual magnet segments that is indicated byarrows in each case;

FIG. 1B shows a schematic spatial illustration of a complete ring-shapedmagnet element according to the invention with depicted azimuthal angleϕ and 3D angle α;

FIG. 2A shows a schematic spatial illustration of the spatial 3D Halbachconfiguration according to the invention, visualized with arrows for therespective magnetization direction;

FIG. 2B shows the spatial illustration of FIG. 2A, but with a flat 2DHalbach configuration in a ring plane according to the prior art;

FIG. 3A shows a schematic sectional illustration through a ring plane ofa magnet arrangement having a flat 2D Halbach configuration of the localmagnetization directions according to the prior art;

FIG. 3B shows the magnet arrangement according to the prior art fromFIG. 3A in a schematic vertical sectional view;

FIG. 4A shows a spatial diagram of the relationship of the designvariables “external radius”, “3D angle” and “half length” for theoptimized design of a magnet arrangement according to the invention;

FIG. 4B shows a spatial diagram of the function of the parameter“weight” as a function of the design variables “external radius” and“half length” for the optimized design of a magnet arrangement accordingto the invention;

FIG. 5 shows a schematic vertical sectional view through a simpleembodiment of the invention having two 3D Halbach rings in amirror-symmetrical arrangement (=exemplary embodiment 1);

FIG. 6 shows a schematic vertical sectional view through a furtherembodiment of the invention having three Halbach rings, wherein thecentral ring has a 3D angle of α=0, while the two outer rings are in amirror-symmetrical arrangement with respect to one another (=exemplaryembodiment 2); and

FIG. 7 shows an even more complex embodiment of the magnet arrangementaccording to the invention having eight magnet rings (=exemplaryembodiment 3).

DETAILED DESCRIPTION

The magnet arrangement 1 according to the invention such as isillustrated in each case schematically in various embodiments in thedrawing finds its main application as part of a magnetic resonanceapparatus—not shown specifically in the drawing—having a permanentmagnet system for generating a homogeneous magnetic field in thedirection of a z-axis in a measurement volume 0 (indicated in FIG. 3B),wherein the permanent magnet system comprises at least two ring-shapedmagnet elements 2, 2′ composed of magnetic material in a ring plane,which are arranged coaxially around the z-axis and are constructed fromindividual magnet segments 3 arranged next to one another in a Halbachconfiguration.

A “traditional” Halbach configuration such as has also already beendescribed in the prior art is illustrated schematically in FIGS. 3A and3B:

FIG. 3A shows a sectional view through a ring plane of such a magnetarrangement having a flat (2D) Halbach configuration of the localmagnetization directions of in each case 2 φ at a location withazimuthal angle f.

FIG. 3B shows the magnet arrangement from FIG. 3A in a schematicvertical sectional view.

The present invention indeed likewise relates to a magnet ring systemcomposed of a plurality of rings in a Halbach configuration, but theouter rings comprise, in the magnetization direction, a spatialcomponent (3D) pointing out of the ring plane. As an essential usefuleffect, this arrangement makes possible a more compact design of themagnet for higher field strength and also a lower leakage field.

Generally, the magnet arrangement 1 according to the presentinvention—as is shown illustratively in FIGS. 1A and 1B is distinguishedby the fact that the magnetization direction of at least two ring-shapedmagnet elements 2, 2′ deviates from the ring plane in such a way thatthe component perpendicular to the ring plane varies cosinusoidally withthe azimuthal angle of the respective ring-shaped magnet element 2, 2′,wherein a 3D angle α determines the deviation of the magnetizationdirections from those of a planar (2D) Halbach ring, and that themagnetization of in each case two ring-shaped magnet elements 2, 2′ ismirror-symmetrical with respect to one another, wherein the mirror planeis the central x-y-plane perpendicular to the z-axis. In FIG. 1B, the 3Dangle α is depicted as the angle between the x-axis and themagnetization direction of that segment which is positioned in thex-direction.

A 3-dimensional distribution of the magnetization directions in a 3DHalbach ring, in the case of which distribution the magnetizationvectors partly project from the ring plane according to the invention,is illustrated in FIG. 2A.

For comparison, FIG. 2B shows the distribution of magnetizationdirections in a “traditional” 2D Halbach ring according to the priorart, in the case of which distribution the magnetization vectors alwayslie within the ring plane.

Preferably, the magnet segments 3 are constructed in the magnetarrangement according to the invention such that the magnetizationdirection of the individual magnet segments 3 follows the formula

Mr=M Cos[α]Cos[ϕ0], Mϕ=M Sin[ϕ0], Mz=M Cos[ϕ0]Sin[α],

wherein the components of the magnetization vector in cylindricalcoordinates denote:M the remanence of the magnet material used in the respectivering-shaped magnet element 2, 2′,ϕ0 the azimuthal angle of the segment midpoint, andα a parameter fixed for the entire ring-shaped magnet element 2, 2′,namely the 3D angle that determines the deviation of the magnetizationdirections from those of a planar Halbach ring.

FIG. 5 shows a first, particularly simple exemplary embodiment:

Example 1

The determination of an optimized geometry of a Halbach magnet accordingto the invention here comprises just two ring-shaped magnet elements 2having mirror-symmetrical magnetization. For illustrating the designprocess according to the invention, the simplest possible case shall beconsidered: two three-dimensional Halbach rings comprising identicalmagnet material are situated symmetrically with respect to the originplane. The inner hole shall be fixedly predefined.

The (half) magnet length, the external radius and the (likewisesymmetrical) 3D angle α then remain as free design variables. If aspecific target field B0 (in the example, B0=Br=1.4 T was chosen given ahole having a radius of 24 mm) and homogeneity of the lowest order(vanishing second field order B2=0) are demanded, then the degrees offreedom decrease to 1.

This is illustrated in the graph in FIG. 4A: the first area A shows allcombinations of the design variables for which the target field B0 isattained; the second area B shows all combinations for which the secondfield order B2 vanishes. The external radius of the Halbach ring in [mm]is plotted on the X-axis. Y denotes the half length of the magnet in[mm]. The 3D angle is indicated in radians on the Z-axis.

That curve on which both demands are met results as a line ofintersection. That point on the line which minimizes the total weight ofthe magnet is now sought for defining the current design.

The graph in FIG. 4B shows the weight of the magnet arrangement as afunction of magnet length and external radius. The external radius ofthe Halbach ring in [mm] is plotted on the X-axis, Y once again denotesthe half length of the magnet in [mm], and the resulting weight isindicated on the Z-axis. If the curve determined above is transferred tothis graph, then it is evident that it rises towards the edges, while itassumes a minimum in the central region. This point corresponds to thedesign optimized in the sense of the invention.

FIG. 6 shows a further, still relatively simple exemplary embodiment:

Example 2

The permanent magnet in a Halbach configuration here comprises threerings with predefined remanence M=B0=1.4 T, wherein the central ring 2 ahas a 3D angle of α=0. The two outer rings 2 are once againmirror-symmetrical with respect to one another in terms of themagnetization.

Essential Boundary Conditions for Exemplary Embodiment 2:

-   -   B0=1.4 T (60 MHz), 48 mm hole    -   second and fourth field orders vanish    -   Br=1.4 T (NdFeB)    -   weight 13 kg    -   α=0.15 in the outer rings, planar Halbach ring in the centre

FIG. 7, finally, shows a somewhat more complex exemplary embodiment:

Example 3

The permanent magnet in a Halbach configuration here comprises eightrings with predefined remanence M=B0=1.9 T, wherein the central ringshave a 3D angle of α=0. The laterally outer rings 2, 2′ aremirror-symmetrical with respect to one another in pairs in each case inthe magnetization direction. The both radially outermost and laterallycentral ring 2 a having a 3D angle of α=0 is adjoined radially inwardlyby a further laterally central ring 2 a′ having a 3D angle of likewiseα=0. In this example, the flat, radially innermost ring-shaped magnetelements 2 b adjoining the radially inner 3D Halbach rings 2′ from innerareas have a homogeneous magnetization with the 3D angle α=71 Theserings supplement the total magnetic field and furthermore result in evengreater homogeneity of the magnetic field generated.

Essential Boundary Conditions for Exemplary Embodiment 3:

-   -   B0=1.9 T (80 MHz), 24 mm hole    -   second, fourth and sixth field orders vanish    -   Br=1.4 T and 1.3 T, respectively, for radially inner rings        (NdFeB)    -   weight 14 kg    -   α=0.62 and 0.80 in the axially outer rings 2 and 2′,        respectively, laterally homogeneously magnetized in the radially        innermost rings 2 b, planar Halbach rings 2 a, 2 a′ axially in        the centre

It is clearly evident in Examples 2 and 3 that, with the configurationaccording to the invention of the magnet rings and an adapted 3D angle αin the magnetization direction, magnets having a high remanence of up to1.9 T in conjunction with a very low weight (here: 14 kg) areproducible. Comparable designs composed of “traditional” planar Halbachrings weigh 14 kg (Example 2) and 20 kg (Example 3). At the same time,the magnet in Example 3 is configured in such a way that magnetic fieldinhomogeneities up to the 6^(th) order vanish, and still up to the4^(th) order in Example 2.

LIST OF REFERENCE SIGNS

-   0 Measurement volume-   1 Magnet arrangement-   2; 2′ Ring-shaped magnet elements having 3D Halbach magnetization-   2 a; 2 a′ Ring-shaped magnet elements having 2D Halbach    magnetization-   2 b Further ring-shaped magnet elements having 2D Halbach    magnetization-   3 Magnet segments

Physical Variables

-   x, y, z Cartesian coordinates-   ϕ0 Azimuthal angle of the segment midpoint-   α 3D angle-   M Remanence-   μ Permeability-   HcJ Coercivity-   Tk Temperature coefficients-   n Order of the far field coefficients-   B0 Target magnetic field-   A First area-   B Second area

LIST OF REFERENCES

Documents taken into consideration for the assessment of patentability

-   [1] U.S. Pat. No. 10,018,694 B2-   [2] US 2010/013473 A1-   [3] U.S. Pat. No. 4,837,542-   [4] US 2015/0061680 A1

What is claimed is:
 1. Magnet arrangement in a magnetic resonanceapparatus comprising: a permanent magnet system configured to generate ahomogeneous magnetic field in a direction perpendicular to a z-axis in ameasurement volume, wherein the permanent magnet system comprises atleast two ring-shaped magnet elements containing magnetic material in aring plane, which are arranged coaxially around the z-axis and which areconstructed from individual magnet segments arranged in a Halbachconfiguration, wherein the magnetization direction of at least tworing-shaped magnet elements deviates from the ring plane such that thecomponent perpendicular to the ring plane varies with the azimuthalangle of the respective ring-shaped magnet element, wherein athree-dimensional (3D) angle α determines deviations of themagnetization directions from analogous magnetization directions of aplanar Halbach ring, and wherein the magnetization of each of the tworing-shaped magnet elements is mirror-symmetrical with respect to theother, wherein the mirror plane is the central x-y-plane perpendicularto the z-axis, wherein the ring-shaped magnet elements are constructedfrom the magnet segments arranged next to one another and are composedof magnetic material, and wherein magnetization directions of the magnetsegments with respect to their outer surfaces parallel to the respectivering plane in each case differs from that of two adjacent magnetsegments in the ring-shaped magnet element.
 2. Magnet arrangementaccording to claim 1, wherein the magnet segments are constructed suchthat the magnetization direction of the individual magnet segmentsfollows the formulaMr=M Cos[α]Cos[ϕ0], Mϕ=M Sin[ϕ0], Mz=M Cos[ϕ0]Sin[α], wherein thecomponents of the magnetization vector in cylindrical coordinatesdenote: M the remanence of the magnet material used in the respectivering-shaped magnet element, ϕ0 the azimuthal angle of the segmentmidpoint, and α a parameter fixed for the entire ring-shaped magnetelement, namely the 3D angle that determines the deviation of themagnetization directions from the analogous magnetization directions ofa planar Halbach ring.
 3. Magnet arrangement according to claim 1,wherein the magnet segments are produced from a hard-magnetic materialhaving a high remanence M, wherein 1.5 T>M>0.7 T, and having a lowpermeability μ in the range of 1.0<μ<1.5.
 4. Magnet arrangementaccording to claim 3, wherein the magnet segments are produced fromNdFeB.
 5. Magnet arrangement according to claim 1, wherein the magnetsegments arranged in a region of high field strengths are produced froma high-coercivity material having a coercivity HcJ in the range of 2800kA/m>HcJ>1500 kA/m.
 6. Magnet arrangement according to claim 1, whereinthe magnet segments are produced from a temperature-compensatedpermanent magnet material having a temperature coefficient Tk in therange of 0%/K>Tk>−0.05%/K.
 7. Magnet arrangement according to claim 5,wherein the magnet segments are produced from SmCo.
 8. Magnetarrangement according to claim 1, further comprising at least onefurther ring-shaped magnet element as a planar Halbach ring, where α=0,arranged coaxially with respect to the at least two ring-shaped magnetelements, which are arranged coaxially around the z-axis.
 9. Magnetarrangement according claim 1, further comprising at least one furtherring-shaped magnet element as a laterally homogeneously magnetized ring,where α=π, arranged coaxially with respect to the at least tworing-shaped magnet elements, which are arranged coaxially around thez-axis.
 10. Magnet arrangement according claim 1, wherein thering-shaped magnet elements are constructed such that far fieldcoefficients of low order n≤6 vanish.
 11. Magnet arrangement accordingclaim 1, wherein the ring-shaped magnet elements are constructed suchthat the dipole moment vanishes.
 12. Magnet arrangement according claim1, wherein the ring-shaped magnet elements are arranged concentricallyaround the z-axis, and a radially inner one of the ring-shaped magnetelements has a higher coercive field strength than do radially outerones of the ring-shaped magnet elements.
 13. Magnet arrangementaccording to claim 1, wherein the magnet segments of each ring-shapedmagnet element have one same outer shape.
 14. Magnet arrangementaccording to claim 1, wherein the magnet segments of each ring-shapedmagnet element have a trapezoidal prism shape.
 15. Magnet arrangementaccording to claim 1, wherein the magnet segments of each ring-shapedmagnetic element are arranged directly adjacent to each other in anassembled state of the magnet arrangement.
 16. Magnet arrangement in amagnetic resonance apparatus comprising: a permanent magnet systemconfigured to generate a homogeneous magnetic field in a directionperpendicular to a z-axis in a measurement volume, wherein the permanentmagnet system comprises at least two ring-shaped magnet elementscontaining magnetic material in a ring plane, which are arrangedcoaxially around the z-axis and which are constructed from individualmagnet segments arranged in a Halbach configuration, wherein themagnetization direction of at least two ring-shaped magnet elementsdeviates from the ring plane such that the component perpendicular tothe ring plane varies with the azimuthal angle of the respectivering-shaped magnet element, wherein a three-dimensional (3D) angle αdetermines deviations of the magnetization directions from analogousmagnetization directions of a planar Halbach ring, and wherein themagnetization of each of the two ring-shaped magnet elements ismirror-symmetrical with respect to the other, wherein the mirror planeis the central x-y-plane perpendicular to the z-axis, wherein thering-shaped magnet elements are constructed from the magnet segmentsarranged next to one another and are composed of magnetic material,wherein magnetization directions of the magnet segments with respect totheir outer surfaces parallel to the respective ring plane in each casediffers from that of two adjacent magnet segments in the ring-shapedmagnet element and wherein the magnet segments of each ring-shapedmagnetic element are arranged directly adjacent to each other in theassembled state and the magnet segments are constructed such that themagnetization direction of the individual magnet segments follows theformulaMr=M Cos[α]Cos[ϕ0], Mϕ=M Sin[ϕ0], Mz=M Cos[ϕ0]Sin[α], wherein thecomponents of the magnetization vector in cylindrical coordinatesdenote: M the remanence of the magnet material used in the respectivering-shaped magnet element (2, 2′), ϕ2 the azimuthal angle of thesegment midpoint, and α a parameter fixed for the entire ring-shapedmagnet element (2, 2′), namely the 3D angle that determines thedeviation of the magnetization directions from the analogousmagnetization directions of a planar Halbach ring.
 17. Method forproducing a magnet arrangement, comprising: a) predefining a targetmagnetic field B0 and a required number of ring-shaped magnet elementscomposed of known magnet material and a desired internal diameter of acentral hole of the magnet; b) determining a desired homogeneity andleakage field properties by equating to zero at least one field order ofthe central or far field expansion; c) determining free designparameters, including geometry parameters of the ring-shaped magnetelements and 3D angles α of the ring-shaped magnet elements, byoptimizing the magnet volume under the constraints from steps a) and b);and d) determining a desired weight as a function of the designparameters determined under step c).
 18. Method according to claim 17,wherein in step c) the field orders and the magnet volume are calculateddirectly from the design parameters by way of analytical formulae. 19.Method according to claim 17, wherein individual magnet segments areproduced in defined magnetization directions in a manner complying withthe 3D angles α and the Halbach angle before the magnet segments areassembled to form ring-shaped magnet elements.